# What are the steps for simplifying radicals?

Jul 6, 2018

See if you can factor out a perfect square

#### Explanation:

In general, when we simplify radicals, we want to factor out a perfect square. For instance:

Let's say we're simplifying the radical $\sqrt{84}$:

Because of the radical law, we can rewrite a radical expression $\sqrt{a b}$ as $\sqrt{a} \cdot \sqrt{b}$.

In our example, we can rewrite $84$ as $4 \cdot 21$. We now have the radical

$\sqrt{4 \cdot 21} = \sqrt{4} \cdot \sqrt{21} = 2 \sqrt{21}$

Since $21$ has no perfect square factors, we cannot factor it any further.

The same goes if we had $\sqrt{54}$. We can rewrite $54$ as $9 \cdot 6$, which allows us to separate the radical as

$\sqrt{9} \cdot \sqrt{6} \implies 3 \sqrt{6}$

Once again, $6$ has no perfect square factors, so we are done.

Let's solidify this further with another example:

$\sqrt{162}$

We can rewrite $162$ as $81 \cdot 2$, which allows us to separate the radical as

$\sqrt{81} \cdot \sqrt{2} \implies 9 \sqrt{2}$

Hope this helps!